Many monochrome and color digital imaging systems have components that perform pixel and line raster subsampling for the purpose of reducing the amount of image data for storage, transmission, or display. NTSC television is an example wherein filtering and rectangular subsampling of chrominance data as well as line subsampling and interlaced display of the image are used to reduce the required system bandwidth.
Other examples are image subband coding and pyramid coding wherein a bank of low-pass and high-pass filters and image subtraction are used with subsampling to isolate and independently quantize certain image frequency regions.
In most applications, the filtering and subsampling are separable in the horizontal and vertical directions with simple one-dimensional filters that avoid spatial aliasing. This is illustrated in FIG. 1, which shows the Nyquist boundaries (N.sub.x, N.sub.y) of a rectangularly sampled input image and the filtered and subsampled Nyquist boundaries due to separable filtering and 2:1 integer subsampling. Four rectangular Nyquist regions can be isolated by having horizontal and vertical low-pass and high-pass filters. These are represented in FIG. 1 by L/L, L/H, H/L, and H/H. The signal flow diagram is shown in FIG. 2 where the .dwnarw.2 symbol represents 2:1 subsampling. Although simple to implement, it is well known that separable decomposition of the input Nyquist region has quality disadvantages for reducing image data. The reasons are related to observed symmetries of image data and the preferred symmetry of the human visual system. FIG. 3a shows a typical power contour in the spatial frequency domain for one color of a digitally scanned image. The predominance of horizontal and vertical image modulation is due in part to the high degree of rectangular symmetry in man-made and naturally occurring objects, but also to the modulation transfer function or MTF of digital scanners that results from rectangular sensor elements and anisotropic optics.
The MTF of the human visual system is also anisotropic with the well documented decrease in acuity at 45.degree. and 135.degree. as shown in FIG. 3b. This preferred symmetry has been used to design reduced resolution, single-chip color sensor arrays for electronic cameras by placing red, green, and blue sensitive pixels in periodic, non-rectangular arrangements to better match image symmetry and to minimize visual resolution loss. There have also been numerous attempts to take advantage of this preferred symmetry in television systems to maintain the current bandwidth and improve the spatial-temporal quality, and to develop systems that allow for auxiliary channels to convert NTSC quality signal to high-definition television signals. In addition, non-rectangular symmetry has been used in image subband coding to improve the rate-distortion performance of image compression systems. To date, all of these methods have used non-separable, two-dimensional filters and diamond or quincunx subsampling to filter or decompose the image. A good, general presentation of this for television signals is given in a 1981 Independent Broadcasting Authority (IBA) Report, 112/81, May, 1981, by G. Tonge. Although non-separable, two-dimensional filters are quite general and have the flexibility to produce the desired filter responses, they are difficult to design, and more importantly difficult to implement requiring order M.sup.2 multiplies and additions per subsampled pixel for an MxM filter. Separable filtering and subsampling has significant implementation advantages because the required processing is reduced to order M with Mx1 and 1xM filters. Since M often ranges from 7-11 for image processing applications, this can be an order of magnitude reduction. A novel use of cascaded, separable filters to generate the non-rectangular, diamond symmetry of FIG. 3a was introduced by E. Guttner in U.S. Pat. No. 4,713,688, entitled "Method For Increasing Resolution Of A Compatible Television System", which issued Dec. 15, 1987 to equilibrate the horizontal and vertical resolution of color television while maintaining bandwidth compatibility with existing systems. The system required a higher resolution TV camera with a two-fold increase in spatial sampling, and used diagonal one-dimensional filters and offset modulation to produce a low-pass, diamond subsampled image with equal line and pixel resolution. Although closest to the present invention, all filtering was low-pass and the higher resolution information of the input camera was discarded. Schreiber, of the Massachusetts Institute of Technology expanded this concept in U.S. Pat. No. 4,979,041, entitled "High Definition Television System", which issued Dec. 18, 1990 to the use of non-rectangular quadrature mirror filters to decompose the image into subbands with the low-pass subbands being compatible with the bandwidth of current television channels and receivers, and the high-pass subbands providing a "bridge" to enhanced definition and high definition television (EDTV and HDTV). He proposed a one-dimensional version of the quadrature mirror filtering by "diagonally addressing frames of image data held in a frame store and passing the diagonally-addressed data through vertical and horizontal filters". The disadvantage of this approach, as compared to the present invention, is that it requires a complete frame store at the transmitter and receiver, and it is limited to diamond symmetry, and without the upsampling step of the present invention can cause severe aliasing in the subbands. This will be described in more details later in the specification.